7-3 Similar Polygons
Similar Polygons
When drawing pictures we do not always draw pictures to actual size. We
draw them to scale. To draw something to scale means to draw it in the
right shape but in a convenient size. Two figures drawn this way are
called similar.
Two polygons are similar if there vertices can paired so that :
(1) ALL Corresponding angles are congruent
(2)
corresponding sides are in proportion. (Their lengths have the same
ratio)
When referring to similar polygons, their corresponding vertices must be listed
in the same order.
Similar Polygons
Y
S
R
T
X
Z
P
Q
20
V
By definition of similar polygons we have:
s  y
,
t  z
32
W
p  v, q  w
,
r  x
Similar polygons
Similarity has some of the same properties as equality and congruence.
Similarity is reflexive, symmetric, and transitive.
If two polygons are similar, then the ratio of the lengths of two
corresponding sides is called the Scale Factor of the similarity.
Similar Polygons
Y
S
R
T
X
Z
P
20
Q
V
32
W
Because we have similar polygons that means the ratios must be the same so
pq qr rs st tp




vw wx xy yz zv
Similar Polygons
Y
S
R
T
X
Z
P
20
Q
V
32
W
Since we know the length of similar pieces we can come up with the scale factor
pq 20

vw 32
Similar Polygons
Y
S
R
T
X
Z
P
20
Q
V
32
W
Since we know the length of similar pieces we can come up with the scale factor
pq 20 5


vw 32 8
The scale factor is
5
8
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
a)
DC
D 'C '
C’
z
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
a)
DC 20

D' C ' 30
C’
z
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
a)
b)
DC
20 2


D' C ' 30 3
C’
z
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
a)
b)
DC
20 2


D' C ' 30 3
2 x

3 21
C’
z
y
2 8

3 y
2 10

3 z
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
a)
b)
DC
20 2


D' C ' 30 3
2 x

3 21
x = 14
C’
z
y
2 8

3 y
y = 12
2 10

3 z
z = 15
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
c. Perimeter of quad ABCD =
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
c. Perimeter of quad ABCD = 10 + 20 + 8 + 14
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
c. Perimeter of quad ABCD = 10 + 20 + 8 + 14 = 52
Perimeter of quad A’B’C’D’ =
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
c. Perimeter of quad ABCD = 10 + 20 + 8 + 14 = 52
Perimeter of quad A’B’C’D’ = 15 + 30 + 12 + 21 =
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
c. Perimeter of quad ABCD = 10 + 20 + 8 + 14 = 52
Perimeter of quad A’B’C’D’ = 15 + 30 + 12 + 21 = 78
d. Ratio of perimeters
52

78
y
A’
21
B’
Similar Polygons
D
20
Quad. ABCD ~ A’ B’ C’ D’.
Find
C
10
8
a.
b.
c.
d.
The scale factor
values of x,y,z
Perimeters of the two quadrilaterals
The ratio of the perimeters
A
B
x
D’
30
C’
z
c. Perimeter of quad ABCD = 10 + 20 + 8 + 14 = 52
Perimeter of quad A’B’C’D’ = 15 + 30 + 12 + 21 = 78
d. Ratio of perimeters
52 2

78 3
y
A’
21
B’